CN103279591B - Based on the method for topological optimization design under the solid weight pressure load of extra cell - Google Patents
Based on the method for topological optimization design under the solid weight pressure load of extra cell Download PDFInfo
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Abstract
The invention discloses a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell, for solving the low technical matters of existing method of topological optimization design optimum results performance.Technical scheme introduces extra cell on the surface of contact of solid mass and supporting construction, is loaded on extra cell by solid mass pressure load.Even if in process of topology optimization, borderline material changes like this, but because all nodes of surface of contact are not directly connected with pressure load, but be connected with extra cell, so the size and Orientation of pressure load also can remain unchanged, optimum results performance is high.Application the inventive method is optimized design, topological optimization iterative process need not upgrade pressure load numerical value at every turn, and material and load contact border remain unchanged, and the compliance of optimization rear support structure is 0.0861mJ; The compliance that document 2 method optimizes rear support structure is 0.0967mJ; Prove that the optimum results performance that the inventive method obtains is better.
Description
Technical field
The present invention relates to a kind of method of topological optimization design, particularly a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell.
Background technology
With reference to Fig. 1 ~ 2.In the field such as Aero-Space, automobile making, structure lightened design under solid weight pressure load is the engineering problem of a quasi-representative, under most topological optimization technology is still confined to solve fixed load, there is the design problem determining border and design domain, namely, in topological optimization iterative process, load does not change; The material boundary of load applying position does not change; Design domain does not change.The difficult point of the design problem on uncertain border is: because the contact area 2 of solid mass and supporting construction may change, thus the total power causing solid mass pressure 1 to be applied in supporting construction changes.The contact area of solid mass and supporting construction
With reference to Fig. 3.Document 1 " TongGaoandWei-hongZhang; Topologyoptimizationofmultiphasematerialstructuresunderd esigndependentpressureloads; InternationalJournalforSimulationandMultidisciplinaryDes ignOptimization.3,297-306 (2009) " discloses the method for topological optimization design under a kind of fixed load compression weight load.Pressure punishment model introduced by document:
Wherein, p
ifor the pressure on Contact surface element i, n
sfor surface in contact number of unit, S
ξfor individual unit pressure load active area, s is penalty coefficient, P
swfor solid weight pressure load, x
imfor the pseudo-density of unit i.In optimizing process after each Optimized Iterative, the pressure load acted on surface in contact unit should recalculate according to corresponding units topology design variable and formula and upgrade finite element model load.
Document 2 " Zhang Weihong, Yang Jungang, Zhu Jihong; Structural topology under pressure load-shape cooperate optimization; Aviation journal; 12nd phase in 2009 " disclose method of topological optimization design under a kind of fixed load.Boundary definition with load contact is non-design domain by document, in topological optimization iterative process, owing to remaining unchanged, so pressure load also can remain unchanged with the material (non-design domain) of compression weight load contact.
Although method disclosed in document 1 can realize the topology optimization design under solid weight pressure load, but its method is too complicated, each topological optimization iteration all will recalculate the pressure load numerical value of effect each unit on the contact surface, affects Optimized Iterative efficiency.Although method disclosed in document 2 can keep the size and Orientation of pressure load constant in topological optimization iterative process, but due to the material contacted with pressure load is defined in order to non-design domain, the structure causing this Topological optimization model to be designed and the material of load contact can not be removed, design domain reduces, design constraint increases, and optimum results performance reduces.
Summary of the invention
In order to overcome the low deficiency of existing method of topological optimization design optimum results performance, the invention provides a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell.The method introduces extra cell on the surface of contact of solid mass and supporting construction, Young modulus 1-2 the order of magnitude larger than the Young modulus of structure of extra cell, the borderline unit contacted with solid mass pressure load is connected with extra cell, solid mass pressure load is not directly loaded in material boundary, but is loaded on extra cell.Even if borderline material changes in process of topology optimization like this, but be not directly connected with pressure load due to all nodes of surface of contact, but be connected with extra cell, so the size and Orientation of pressure load also can remain unchanged.This method can realize the topology optimization design requirement under solid weight pressure load, size and the aspect of maintenance pressure load are constant, but do not upgrade load value in each iteration, affect iteration efficiency, also do not introduce non-design domain, limiting material border is constant, optimum results performance is high.
The technical solution adopted for the present invention to solve the technical problems is: a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell, is characterized in comprising the following steps:
A () sets up finite element model by the cad model of structure; The surface of contact 2 of solid mass and supporting construction defines extra cell, extra cell Young modulus 1-2 the order of magnitude larger than structured material Young modulus; Definition load, is loaded into solid mass pressure 1 load on extra cell.
B () building topology Optimized model is:
findX＝(x
1,x
2,…,x
n)
minΦ(X)
s.t.KU＝F
Wherein, X is the pseudo-intensity vector of unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; G
j(X) be a jth constraint function;
for the upper limit of a jth constraint function; J is the quantity of constraint.
C model is carried out a finite element analysis by (); By optimizing sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition, choose certain optimized algorithm and be optimized design, be optimized result.
The invention has the beneficial effects as follows: because the method introduces extra cell on the surface of contact of solid mass and supporting construction, Young modulus 1-2 the order of magnitude larger than the Young modulus of structure of extra cell, the borderline unit contacted with solid mass pressure load is connected with extra cell, solid mass pressure load is not directly loaded in material boundary, but is loaded on extra cell.Even if borderline material changes in process of topology optimization like this, but be not directly connected with pressure load due to all nodes of surface of contact, but be connected with extra cell, so the size and Orientation of pressure load also can remain unchanged.This method can realize the topology optimization design requirement under solid weight pressure load, size and the aspect of maintenance pressure load are constant, but do not upgrade load value in each iteration, affect iteration efficiency, also do not introduce non-design domain, limiting material border is constant, optimum results performance is high.Application the inventive method is optimized design, topological optimization iterative process need not upgrade pressure load numerical value at every turn, and material and load contact border remain unchanged, and the compliance of optimization rear support structure is 0.0861mJ; And the method applied in document 1, then need to upgrade load value in each iterative process, load contact face is defined as non-design domain by the method in application document 2, and the compliance optimizing rear support structure is 0.0967mJ; The optimum results performance that the method applied in the present invention obtains is better.
Accompanying drawing explanation
Fig. 1 is the structural representation of solid weight pressure load in background technology.
Fig. 2 is solid weight pressure load distribution schematic diagram in background technology.
Fig. 3 is the method schematic diagram solving the use of this problem in background technology list of references 2.
Fig. 4 is the supporting construction schematic diagram of using method of the present invention.
Fig. 5 is the stress model of moulded dimension schematic diagram the inventive method of specific embodiment.
Fig. 6 is the topology optimization design result of specific embodiment application the inventive method.
Fig. 7 is the topology optimization design result of list of references 2 method in specific embodiment application background technology.
In figure, 1-solid mass pressure; The surface of contact of 2-solid mass and supporting construction.
Embodiment
With reference to Fig. 4 ~ 7.For two-dimensional solid compression weight load structure, the present invention is described.Two dimension support physical dimension is long 500mm, high 300mm, and thickness is 1mm, and its Young modulus is 2.1 × 10
5mpa, Poisson ratio is 0.3.Weight quality is 10kg, entirely fixes bottom supporting construction.Design supporting construction, make its rigidity maximum, material usage volume fraction is 30% to the maximum.Method step is as follows:
(a) finite element modeling.
Finite element model is set up: the setting grid length of side is 10mm, grid division by the cad model of structure.Definition load: because weight quality is 10kg, get gravity acceleration g=9.8m/s
2, according to weight and supporting structure contact area, then pressure is 0.196Mpa.Definition boundary condition: whole for supporting construction bottom node degree of freedom is fixed.The surface of contact 2 of solid mass and supporting construction defines extra cell, and extra cell Young modulus is 2.1 × 10
7mpa; Definition load: solid mass pressure 1 load is loaded on extra cell.
B () building topology Optimized model is
findX＝(x
1,x
2,…,x
n)
minΦ(X)
s.t.KU＝F
G(X)-0.3≤0
Wherein, X is design variable---the pseudo-intensity vector of the unit in design domain; N is design variable number; Φ (X) is objective function, is the rigidity of supporting construction in the present embodiment; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; The volume fraction that G (X) is finite element model.
(c) finite element analysis and Optimization Solution.
By finite element soft Ansys, model is carried out a finite element analysis; Sensitivity analysis is optimized again by structure optimization platform Boss-Quattro, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA(GloballyConvergentMethodofMovingAsymptotes) optimized algorithm is optimized design, and be optimized result.
As can be seen from Fig. 6 and Fig. 7 optimum results, carry out the topology optimization design under solid weight pressure load by the inventive method, the borderline unit of load contact can be removed in topological optimization iterative process, and does not change the size of load.Compared with document 1 method, the inventive method does not need to upgrade pressure load in each topological optimization iterative process, decreases topological optimization iteration time; By contrasting can find out with document 2 method, the optimum results compliance that the inventive method obtains is 0.0861mJ, and the optimum results compliance that documents 2 method obtains is 0.0967mJ; The optimum results performance that the method applied in the present invention obtains is better.
Claims (1)
1., based on the method for topological optimization design under the solid weight pressure load of extra cell, it is characterized in that comprising the following steps:
A () sets up finite element model by the cad model of structure; The surface of contact (2) of solid mass and supporting construction defines extra cell, extra cell Young modulus 1-2 the order of magnitude larger than structured material Young modulus; Definition load, is loaded on extra cell by solid mass pressure (1) load;
B () building topology Optimized model is:
findX＝(x
1,x
2,…,x
n)
minΦ(X)
s.t.KU＝F
In formula, X is the pseudo-intensity vector of unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; G
j(X) be a jth constraint function;
for the upper limit of a jth constraint function; J is the quantity of constraint;
C model is carried out a finite element analysis by finite element soft Ansys by (); Be optimized sensitivity analysis by structure optimization platform Boss-Quattro again, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA and be optimized design, be optimized result.
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| CN106096172A (en) * | 2016-06-22 | 2016-11-09 | 西北工业大学 | Load controlled delivery structural topological optimization method |
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| JP2015111352A (en) * | 2013-12-06 | 2015-06-18 | 三菱重工業株式会社 | Structure analysis method |
| CN106202786B (en) * | 2016-07-19 | 2019-05-21 | 大连理工大学 | A kind of filtered variable design method about big L/D ratio cylindrical shell structure topological optimization |
| CN107357974B (en) * | 2017-03-31 | 2020-07-31 | 华侨大学 | Non-uniform fiber reinforced composite material distribution optimization design method |
| CN109760309B (en) * | 2019-01-16 | 2021-03-16 | 北京工业大学 | Manufacturing method of ankle-foot orthosis based on 3D printing technology |
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| CN102117357A (en) * | 2010-12-14 | 2011-07-06 | 深圳市大族激光科技股份有限公司 | Weight-reducing optimal design method for parts of PCB (printed circuit board) numerical control drilling and milling machine |
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| CN102117357A (en) * | 2010-12-14 | 2011-07-06 | 深圳市大族激光科技股份有限公司 | Weight-reducing optimal design method for parts of PCB (printed circuit board) numerical control drilling and milling machine |
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| Title |
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| 多相材料结构拓扑优化：体积约束还是质量约束;高彤等;《力学学报》;20110331;第43卷(第2期);全文 * |
| 静力载荷和随机激励下结构拓扑优化设计;张桥，张卫红，朱继宏;《中国计算力学大会2010暨第八届南方计算力学学术会议》;20101231;全文 * |
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| CN106096172A (en) * | 2016-06-22 | 2016-11-09 | 西北工业大学 | Load controlled delivery structural topological optimization method |
| CN106096172B (en) * | 2016-06-22 | 2019-12-20 | 西北工业大学 | Topological optimization method of load-controllable transfer structure |
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